1. LARGE EDDY SIMULATION
Chin-Hoh Moeng
NCAR

2. OUTLINE
WHAT IS LES?
APPLICATIONS TO PBL
FUTURE DIRECTION

3. WHAT IS LES?
A NUMERICAL TOOL
FOR
TURBULENT FLOWS

4. Turbulent Flows governing equations, known
nonlinear term >> dissipation term
no analytical solution
highly diffusive
smallest eddies ~ mm
largest eddies --- depend on Re- number (U; L; )

5. Numerical methods of studying turbulence
Reynolds-averaged modeling (RAN)
model just ensemble statistics
Direct numerical simulation (DNS)
resolve for all eddies
Large eddy simulation (LES)
intermediate approach

6. LES turbulent flow Resolved large eddies Subfilter scale, small
(important eddies)
Subfilter scale, small
(not so important)

7. FIRST NEED TO SEPARATE THE FLOW FIELD
Select a filter function G
Define the resolved-scale (large-eddy):
Find the unresolved-scale (SGS or SFS):

8. Examples of filter functions
Top-hat
Gaussian

9. Example: An 1-D flow field
Apply filter 
large eddies

10. Reynolds averaged model (RAN)f
Apply ensemble avg 
non-turbulent

11. LES EQUATIONS
Apply filter G
SFS

12. Different Reynolds number turbulent flows
Small Re flows: laboratory (tea cup) turbulence; largest eddies ~ O(m); RAN or DNS
Medium Re flows: engineering flows;
largest eddies ~ O(10 m); RAN or DNS or LES
Large Re flows: geophysical turbulence;
largest eddies > km; RAN or LES

13. Geophysical turbulence
PBL (pollution layer)
boundary layer in the ocean
turbulence inside forest
deep convection
convection in the Sun
…..

14. LES of PBL inertial range, km m mm resolved eddies SFS eddies L
energy input
dissipation

15. Major difference between engineer and geophysical flows: near the wall
Engineering flow: viscous layer
Geophysical flow: inertial-subrange layer; need to use surface-layer theory

16. The premise of LES
Large eddies, most energy and fluxes, explicitly calculated
Small eddies, little energy and fluxes, parameterized, SFS model

17. The premise of LES
Large eddies, most energy and fluxes, explicitly calculated
Small eddies, little energy and fluxes, parameterized, SFS model
LES solution is supposed to be insensitive to SFS model

18. Caution near walls, eddies small, unresolved
very stable region, eddies intermittent
cloud physics, chemical reaction…
more uncertainties

19. A typical setup of PBL-LES
100 x 100 x 100 points
grid sizes < tens of meters
time step < seconds
higher-order schemes, not too diffusive
spin-up time ~ 30 min, no use
simulation time ~ hours
massive parallel computers

20. Different PBL Flow Regimes
numerical setup
large-scale forcing
flow characteristics

21. Clear-air convective PBL
Convective updrafts
~ 2 km

22. Horizontal homogeneous CBL

23. LIDAR Observation
Local Time

24. Oceanic boundary layer
Add vortex force for Langmuir flows
McWilliam et al 1997

25. Oceanic boundary layer
Add vortex force for Langmuir flows
McWilliams et al 1997

26. Add drag force---leaf area index
Canopy turbulence
< 100 m
Add drag force---leaf area index
Patton et al 1997

27. Comparison with observation
LES

28. Shallow cumulus clouds
~ 12 hr
~3 km
~ 6 km
Add phase change---condensation/evaporation

29. COUPLED with SURFACE turbulence heterogeneous land
turbulence ocean surface wave

30. Coupled with heterogeneous soil
Surface model
Wet soil
LES model
Dry soil
the ground
Land model

31. Coupled with heterogeneous soil
wet soil
dry soil
(Patton et al 2003)

32. Coupled with wavy surface
stably stratified

33. U-field
flat surface
stationary wave
moving wave

34. So far, idealized PBLs
Flat surface
Periodic in x & y
Shallow clouds

35. Future Direction of LES for PBL Research
Realistic surface
complex terrain, land use, waves
PBL under severe weather

37. mesoscale model domain
500 km
50 km
LES domain

38. Computational challenge
Resolve turbulent motion in Taipei basin
~ 1000 x 1000 x 100 grid points
Massive parallel machines

39. Technical issues Inflow boundary condition
SFS effect near irregular surfaces
Proper scaling; representations of ensemble mean

40. How to describe a turbulent inflow?

41. What do we do with LES solutions?
Understand turbulence behavior & diffusion property
Develop/calibrate PBL models
i.e. Reynolds average models

42. CLASSIC EXAMPLES
Deardorff (1972; JAS)
- mixed layer scaling
Lamb (1978; atmos env)
- plume dispersion

43. FUTURE GOAL Understand PBL in complex environment
and improve its parameterization
for regional and climate models
turbulent fluxes
air quality
cloud
chemical transport/reaction